The skewness and kurtosis of the projected density distribution function: validity of perturbation theory

We study the domain of validity of Perturbation Theory (PT), by comparing its predictions for the reduced skewness, s_3, and kurtosis, s_4, of the projected cosmological density field, with the results of N-body simulations. We investigate models with different linear power spectra and consider as physical applications both angular galaxy catalogues and weak lensing surveys. We first find that the small-angle approximation for the predicted skewness provides a good match to the exact numerical PT results. On the other hand, results from non-linear simulated catalogues agree well with PT results on quasi-linear angular scales, which correspond to scales larger than about 1 degree in the applications we have considered. We also point out that, on smaller scale, the projection effects tend to attenuate the effects of the strong nonlinearities in the angular skewness and kurtosis.